Question

Question 14: Explain why the point where the two BRFs intersect is a Nash Equilibrium.

Answer 1

Nash equilibrium : An outcome where no player has an incentive to deviate from that strategy given the other player stays with the strategy.

Or

When two players are involved in a game,

Nash equilibrium strategy is the combination of strategies where each players gets his/her best payoff given the other player's strategy.

It means no one person can gain by deviating that strategy. (Unilateral deviations can't achieve higher payoffs)

Best response function (BRF) : BRF shows the profit maximizing quantity for a firm given the quantity chosen by the other firm. For any quantity that firm 2 chooses to produce, BRF of firm 1 shows the best quantity (profit maximizing quantity) for firm 1.

Similarly for any quantity that firm 1 chooses to produce, BRF of firm 2 shows the best (profit maximizing) quantity for firm 2.

At the intersection of two BRFs, it shows a combination of outputs (q_{​​​​​​1},q_{​​​​​​2}​) where each firm is maximizing its profit given the other firm's quantity.

It means q_{​​​​​​1} is the profit maximizing quantity for firm 1 given that firm 2 is producing q_{​​​​​​2} and q_{​​​​​​2} is the profit maximizing quantity for firm 2 given that firm 1 is producing q_{​​​​1}.

No one can earn higher profits by deviating from this combination given that other firm stays at it's quantity.

Precisely, q_{​​​​​​1} is the best for firm 1 given firm 2 is producing q_{​​​​​​2} and q_{​​​​​​2} is best for firm 2 given firm 1 is producing q_{​​​​​​1}.

It's the definition of Nash equilibrium which says each player gets their best payoff (profit in this case) given the other player's strategy (quantities in this case).

Therefore, intersection of two BRFs is called a Nash equilibrium.

15 Prmls output Frrmm BRF 20 25 NU NASH FQUILIBRIDM (a44 30